An object is located so that a virtual image is formed -12.9 cm behind a concave mirror that has a 8 cm focal length. Calculate the object distance.

Question

BlackTom AI · Accepted Answer

We start by noting the given data and the sign convention for mirrors: a concave mirror has a positive focal length, and distances in front of the mirror (toward the object) are taken as positive, while distances behind the mirror are negative for images. The problem states the virtual image is formed 12.9 cm behind the mirror, so the image distance is v = -12.9 cm. The focal length is f = +8 cm.

Use the mirror equation: 1/f = 1/v + 1/u, where u is the object distance (positive if the object is in front of the mirror).

Solve for 1/u: 1/u = 1/f − 1/v = (1/8) − (1/−12.9) = 0.125 + 0.077509 ≈ 0.202509.

Then u = 1 / 0.202509 ≈ 4.938 cm.

Therefore, the object distance is about +4.94 cm, meaning the object is positioned roughly 4.9–5.0 cm in front of the mirror along the principal axis. If you round differently or use fewer significant figures, you may see values near 4.9 cm or 5.0 cm. The key checks are that the image is virtual (v negative) and the focal length is positive for a concave mirror, which together constrain the sign and magnitude of u as found.

In summary, u ≈ +4.94 cm. The sign indicates the object lies in front of the mirror as required by the convention.

An object is located so that a virtual image is formed -12.9 cm behind a concave mirror that has a 8 cm focal length. Calculate the object distance.

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